Years ago when I first started smithing ( 50 Plus yrs. ) it was recommended to use medium carbon steels like 1045 for hot work tools. This was because it would stand up to the thermal cycling better than higher carbon steels. Also the advantage of higher carbon steels being harder didn't mean much since the tempering of a hot cut tool much over a Blue color was impractical. A thin edge of the tool touching 1800 deg metal for any amount of time ruining a higher temper any way.
Now many recommend S7 or H13. These steels stand up remarkably well but are extremely expensive and to truly be tempered properly require a drawn out heat treatment process hard to do properly with just a forge. Although these alloys do stand up well, once they do need to be re-heat treated this slow process needs to be repeated again.
I find alloys like 4140and 5160 to be cost effective and quick to retemper when in the middle of a job. Steels like 5160 can be found for almost nothing ( most auto coil springs ) and 4140 isn't to expensive to purchase. If you live in oil country sucker rods are made from 4140.
These two cheaper alloys make it practical to make duplicate drifts, punches, chisels for large jobs so that if a tool does become damaged you can just pick up a duplicate and continue on. 5160 is perfect for the hobbyist ( cheap and easy to get ) 4140 will actually take more abuse but can cost a little more.
Hope this helps!